On the first 7 quizzes of her physics class, Gabriela got an average score of 82. What does she need on the next quiz to have an overall average of 84?
Answer: Let her score on the next quiz be $x$ The sum of all of her scores is then $7 \cdot 82 + x$ The same sum must also be equal to $8 \cdot 84$ Solve: $x = 8 \cdot 84 - 7 \cdot 82 = 98$.